I think you could start by taking her to see your general pediatrician
. Your pediatrician will help you sort out some of the symptoms your daughter is having and help you decide whether a referral to a child psychiatrist
Children your daughter's age can become depressed. They can also just be suffering from stress related to school or other factors, and these may be easily modifiable (or not) through some directed parenting or by talking to officials at her school. There can also be other conditions, such as attention deficit disorder or learning disabilities, which might be confused with a mood problem.
You pediatrician will probably want to know about how your child is doing in school, whether she has behavioral or discipline problems, what her friendships are like and what her relationships to you and any brothers or sisters is like, etc. They will also ask about any recent stressors, such as divorce or death in the family or a recent move. The answers to these questions will help them get a better sense of your daughter's overall functioning and to identify areas of potential concern. Based on these, they will help you decide what the next step should be.